Question

The mass of the moon is $\frac{1}{81}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

• A. The radius of earth is $\frac{9}{\sqrt{6}}$ of the moon
• B. The radius of moon is $\frac{81}{6}$ of the earth
• C. Moon is the satellite of the earth
• D. None of the above

Answer 1

The correct option is A The radius of earth is $\frac{9}{\sqrt{6}}$ of the moon

Gravitational pull depends upon the acceleration due to gravity on that planet
$M_m=\frac{1}{81}{M}_e,g_m=\frac{1}{6}{g}_e$
By relation, $g=\frac{GM}{R^2}$
$\frac{R_e}{R_m}={(\frac{M_e}{M_m}\times \frac{g_m}{g_e})}^{\frac{1}{2}}={(81\times \frac{1}{6})}^{\frac{1}{2}}$
$\therefore R_e=\frac{9}{\sqrt{6}}{R}_m$